PROBABILITY DISTRIBUTION WITH MULTIPLE ATTEMPTS WITH UNIQUE PROBABILITIES

Question

My problem relates to PROBABILITY. Issue is that I wish to calculate a CDF and/or PDF based on multiple attempts. As example : probability of "k" successes from "n" attempts. This is obvious with a Binomial expansion - but that is of course only applicable if all attempts are with the same Probability of Success. In my case - they are not. I have solved this so far by expanding and calculating all possible outcomes and counting results (!!!) : this is very simple and works fine - but becomes almost unmanageable for (n > about 23). I would really like to go up to about 50. I know there is a better way - but I just cannot find any reference that is useful. Any help or guidance would be greatly appreciated.

Answer 1

Without further information, your direct, brute-force approach is the only way to go....and it will become computationally infeasible rather quickly.

Can you give further details?